Question: Solve for $x$. $11^x=11^4\cdot11^5$ $x=$
Solution: When powers have the same base, $x^m\cdot x^n=x^{m+n}$. Let's expand the powers for ${11^x}={11^4}\cdot11^5}$. $\begin{aligned} &={\underbrace{11\cdot11\cdot11\cdot11}_\text{4 times}}\cdot\underbrace{11\cdot11\cdot 11\cdot 11\cdot 11}_\text{5 times}} \\\\\\ &={\underbrace{11\cdot 11\cdot 11\cdot 11\cdot 11\cdot 11\cdot 11\cdot 11\cdot11}_{x\text{ times}}} \\\\ \end{aligned}$ $x=9$